Some properties of the dynamic intermediate state in type 1 superconductors

SOME PROPERTIES OF THE DYNAMIC

INTERMEDIATE STATE IN TYPE I

SUPERCONDUCTORS

Richard A. Lerski

A Thesis Submitted for the Degree of PhD

at the

University of St Andrews

1974

Full metadata for this item is available in

St Andrews Research Repository

at:

http://research-repository.st-andrews.ac.uk/

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10023/14669

SOME PROPERTIES OF THE DYEAMIG INTERMEDIATE STATE IN TYPE I SUPERCONDUCTORS

A Thesis presented by

Richard A« herski^ B,Sc., to the

University of St, Andrews in application for the Degree

ProQuest Number: 10171259

All rights reserved

INFORMATION TO ALL USERS

The quality of this reproduction is dependent upon the quality of the copy submitted.

In the unlikely event that the author did not send a com plete manuscript and there are missing pages, these will be noted. Also, if material had to be removed,

a note will indicate the deletion.

uest

ProQuest 10171259

Published by ProQuest LLO (2017). Copyright of the Dissertation is held by the Author.

All rights reserved.

This work is protected against unauthorized copying under Title 17, United States C ode Microform Edition © ProQuest LLO.

ProQuest LLO.

789 East Eisenhower Parkway P.Q. Box 1346

T U

DEOhARATION

I hereby certify that this thesis has been composed by me^ and is a record of work done by me, and has not previously been presented for a Higher Degree,

The research was carried out in the School

of Physical Sciences in the University of St, Andrews, under the supervision of Professor J*F, Allen, F,R,S,

CERTIFICATE

I certify that Richar’d A, Lerski, B,Sc,, has spent nine terms at research work in the School of Physical Sciences in the University of St, Andrews

under my direction, that he has fulfilled the conditions of the Resolution of the University Court, I

967

, Ho, 1, and that he is qualified to submit the accompanying thesis in application for the Degree of Doctor of Philosophy,

CAREER

il

1

I matriculated in the University of J

Edinburgh in October, I

966

, and obtained Upper Second Class Honours in Physics in

1970

.

In October, 1970, following the award of an

8

,R,C* Research Studentship, I was enrolled as a research student under Resolution of the University Court, I

967

, No, 1, as a candidate for the degree of Ph,Dd

ACKNOWLEDGEMENTS

The author wishes to express his gratitude to Professor J,E, Allen, E,R,S, for his helpful supervision, to Mr, J,G,M, Armitage for many useful suggestions, and to Dr, H, Kirohner for his invaluable advice on the application of the magneto-^optio method and for the gift of a quantity of europium sulphide.

He thanks Mr, R,H, Mitchell for a plentiful

supply of liquid helium, and the workshop staff of the

School of Physical Sciences for skilful technical assistance. He especially wishes to thank his wife, Janice, for her careful typing of all of this thesis.

I

I

ABSTRACT

The high resolution magneto-optic method using the Faraday effect in thin films of EuS:EuFg has been used to observe the dynamic

intermediate state induced by the passage of an electric current or a heat current through thin slabs of the superconductors Pb, In and Sn,

The ease with which the various intermediate state topologies could be made to move has been studied and several features of the interaction of moving flux with pinning sites have been noted.

In the case of the current induced motion the measured characteristics of flux flow velocity versus current have been found to exhibit two

distinct regions. Firstly, a linear region where the observed

velocity was found to agree reasonably well with the predictions of the recent general theory of Andreev and Dshikaev when allowance was made for the effects of pinning by the introduction of a velocity independent pinning force. Secondly, a curved region was found for currents close to the critical current J in agreement with earlier work using other methods of observation. Possible reasons for the existence of this

curvature were examined in detail, and it was found that a phenomenological model based on the presence of a Gaussian distribution of critical current values throughout the sample could account satisfactorily for the

observations. The presence of such a Gaussian distribution was

confirmed by observing the variations in distance travelled by a domain subjected to a pulsed driving current. The curvature was found in disagreement with the theory of thermal activation and no evidence could be found for the presence of a velocity dependent pinning force.

In the case of the thermally induced motion which was

Andreev and Dahikaev in their general theory, which acts in a direction parallel to the heat flow, was found to be effective at low temperature8

(T ^ Uo2K) but to be negligible at high temperatures. The magnitude of

the velocity produced by this mechanism agreed reasonably well with the theory at low temperatures but was in complete disagreement at high

CONTENTS

SECTION

1

0

INTRODUCTION ^

1.1 Discovery and basic theory of superconductors

1.2 Siurface energy - Type I and Type II superconductors 1.5 Magnetic properties of Type I superconductors

1 .Ij. The intermediate state - static and dynamic properties 1.5 Methods of observation of the intermediate state

II. APPARATUS and EXPERIMENTAL DETAILS 2

01

Introduction

2.2 The cryostat

2.5

Construction of the sample mount

2.1|. Requirements of the magneto-optic experiment 2.5 Preparation of the EuSiEuEg films

2.6 Optical equipment

2.7 Performance of the apparatus

2.8 Measurement of the sample conductivity III. SAMPLES

5.1 Introduction 5.2 Lead

5,5 Tin 5«ii. Indium '

IV. THE THEORY OF THE DYNAMIC INTERMEDIATE STATE \

Ji

0

1 Introduc tion it.2 Early theories

iio5 General theory of Andreev and Dzhikaev

it.ij. An addition to the theory of Andreev and Dzhikaev V. THE ROLE OF PINNING IN LIMITING FLUX MOTION

5.1 Introduction

5.2 The effect of pinning on experimental data

PAGE

1.1

1.5 1.5 1.6

1 .1 1

1 1 . 1

11.1 11.5 11.5

1 1 .7

../r.C' ..f"'. I:'.,

VI

0

EXPERIMENTAL RESULTS FOR CURRENT INDUCED MOTION

6

.1 Introduction VI.1

6.2 General features of the flux motion VI,1 6.3 Domain velocity versus current characteristics VI

,6

6

,Jt Nature of the motion near J - J "VI,10

6,5 Conclusions VI,20

VII, EXPERIMENTAL RESULTS FOR TEMPERATURE GRADIENT INDUCED MOTION

7.1 Introduction VII,1

7.2 The observation of pure thermally induced motion VII,2 7.3 The observation of current assisted motion VII

,6

7,it Conclusions VII

,8

VIII, SUMMARY

8.1 Discussion of results VIII,1

8.2

Suggestions for further work VIII,3

REFERENCES

1

A

J

$ %

i

-I

LIST OF SYMBOLS

B magnetic flux density,

B flux density outside specimen, B^ flux density inside specimen, D demagnetization constant, E electric field strength,

Ej domain energy due to influence of Lorentz force, E^ pinning energy,

applied magnetic field strength, |

critical magnetic field strength, field strength inside specimen,

critical magnetic field strength at 0 K, h reduced applied field (h -■=

J electric current density, surface current density, critical current density*

J average critical current density,

L latent heat of the transition normal to superconducting, M magnetization (magnetic moment per unit volume).

Q heat current density,

Q, critical heat current density, R flux creep rate,

S standard deviation of the critical current distribution, T temperature,

T^ superconducting transition temperature, V domain velocity or Verdet constant,

Vj domain velocity due to influence of current J, V critical domain velocity.

Vp domain velocity when Ej - E^.

domain velocity due to influence of normal state thermo­ electric power,

V^ domain velocity due to influence of the mechanism of

Andreev and Dzhikaev,

X fraction of metal in normal state,

Xg fraction of metal in superconducting state.

d surface energy per unit area,

0

^ numerical value of the thermoelectric power of the normal state,

a electrical conductivity.

\ penetration depth, or wavelength,

J coherence length,

^ order parameter,

^ order parameter,

p, permeability,

A surface energy parameter (or = A ^ )„

thermal conductivity of normal state,

'K^ thermal conductivity of superconducting state,

J^ik resistivity tensor,

*^ik thermoelectric tensor,

(

5

” (J ) deviation of the effective average critical current value

NOTE

In all the diagrams and photographs of the

intermediate state in this thesis the superconducting regions are dark and the normal regions light.

'Y.''

Never seen the like since I "been horn^ the people keep a-coming;, and the train's done gone

loi

CHAPTER 1 - INTRODTJGTION

loi Discovery and ’basic theory of superoonductors

Superconductivity was first discovered and so natned hy Kamerlingh Onnes in I

9

II

0

Soon after his successful liquefaction of helium he became engaged in investigating the behaviour of the electrical resistance of various metal-s» Dur'ing measurements on a sample of mercury he observed that its resistance dropped from 0,08 Q _{at about j^K to less than 5 x 10"^Q}

at and that this drop occurred over a temperature interval of CUOIK, The most recent measurements of the resistance of the superconducting state by Quinn and Ittner (I

962

) indicate an upper limit to the resistivity of

^.6

X 10 ^^M,om, Thus we arrive at the first characteristic property of a superoonductors its electrical resistance, for all practical purposes, is zero below a well defined transition temperature T^i

The second and perhaps the more interesting characteristic property of a superconductor is that at any temperature T below T^ the application of a critical magnetic field H^ destroys the superconductivity and causes the resistance to revert to that of the normal state (Kamerlingh Onnes 1.1913))o This critical field is found experimentally to obey, to within a few percent, the relation

He = (1 - (T/Te)^), (1,1)

where H is the value of the critical field appropriate to T “ OK,

For twenty years after their discovery it was assumed that the magnetic properties of superconductors were solely those to'be expected for a perfect conductor, i,e, the magnetic field inside a superconductor should remain constant with time (B - 0), This follows from Ohm's law £ “ oE and the Maxwell equation Vx E = - B/c when a oo

Indeed it was not until 1933 that Meissner and Ochsenfeld (,1933)

discovered that superconductors have the additional property in equilibrium of never possessing an internal flux, regardless of the path by which the

■'■?i

...% 1.2

superconducting state is reached. That is to say, not only does a superconductor not allow any variation of flux with time to occur within

it (B = O), as would he expected for a perfect conductor, hut there is

also no flux within it (B ~ O). This is known as the Meissner effect. The discovery of the Meissner effect dispelled the doubts which had existed up to that time about whether the superconducting transition was a reversible one, and led to the development of a thermodynamic treatment by Gorter and Casimir (193I|. a, b). They regarded the superconductor as a system of two fluids - (a) the superelectrons which flow with no

resistance, and (b) the normal electrons, and imagined that it possessed an order characterised by a parameter Cxi which could be thought of as the fraction of electrons which had. become superelectrons.

About the same time, the brothers Fritz and Heinz London (1935 a, b) developed a model which described the Meissner effect by assuming that a magnetic field (less than critical) applied to a superconductor decays exponentially inwards from its surface, with a characteristic distance

X (where ^ ^surface^ called the penetration depth. Experimentally

~k (T = ok) is around 10 «^rising to A --oo at T^.

These two theories have been very successful in simple problems where size or surface effects are unimportant and, In particular, they provide a good description of what is called the intermediate state.

An important point noted by H. London (1935) is that the exclusion of an external field does not lead to the lowest energy state unless there is a positive surface energy on the boundary between normal and superconducting phases. This is because the energy of a superconductor increases by

a (per unit volume) in the presence of an excluded magnetic field

8n

and a lowering of this energy increase could easily be achieved by a

splitting of the superconductor into normal and superconducting laminae of widths X and < A respectively. The free energy of the superconducting laminae would be lowered since being thinner than the penetration

depth the magnetic field

I

;«

4

1.3 ^

€:

would penetrate their entire width, while the free energy of the normal ;f

:a

regions would he negligible because of their extreme narrowness. However,

such a fine splitting is not observed experimentally so a positive surface

■'.4f

energy must exist on the phase boundaries to preclude it. $

3

.

The existence of this high surface energy and problems in the London model concerning the entropy density at the surface of the superconductor led Pippard (1950, 1951? 1953) to propose a modification of the London model in which the order parameter tu did not change abruptly at a phase boundary but rather gradually over a characteristic distance ^ which he

0

added the coherence length. He found J to be about 20 times the penetration depth, or of the order of lO^^om, This difference between the penetration depth and the coherence length explained the existence of the surface energy since at a boundary the condensation energy of the superconducting state falls off with a characteristic length ^ while the magnetic energy of the normal state falls off with characteristic ^ length A, thus leading to an energy surplus,

A phenomenological quantum mechanical theory compatible with Pippard *s approach was developed by Ginzburg and Landau (I

950

) by expressing the free energy of the superconductor in terms of an order parameter c p

and minimising it with respect to this parameter.

Finally, in 1957 a complete microscopic theory of superconductivity was given by Bardeen, Cooper and Sohrieffer (1957) based on the pairing of electrons of opposite spin and momentum which condensed into a lower energy state than unpaired electrons (FrÜhlich (I

95

O), Cooper (1956)), Although the BOS theory correctly predicts most, if not all, of the electromagnetic and thermal properties of superconductors, it is not important for the results of this work and will not be discussed further.

1 » 2 Surface energy - Type I and Type II superconductors

As previously discussed, H. London (

1935

) pointed out the necessity

I0I4

of the existence of a positive surface energy at a boundary between

superconducting and normal regions and since this idea was supported by the Pippard and Ginzburg-Landau theories, for many years all

superoonductox’B were assumed to exhibit this property. This was despite the fact that deviations from the 'ideal' Meissner behaviour had been

observed in superconducting alloys (Mendelssohn and Moore (1935))« j These deviations were at this time generally considered to be impurity

effects and of little fundamental interest, and consequently it was not -4 until

1957

upon the publication of Abrikosov's paper on the possibility

of the existence of a new cldss of 'Type II' superconductors, that it

was realised that these deviations were in fact.fundamental properties -4 of this new type. It is implicit in Abrikosov's theory that these

Type II materials should exhibit a negative surface energy due to their coherence length being less than their penetration depth.

The reason why this behaviour is observed in alloys is that the

electron mean free pa,th and hence the coherence length is reduced by the , addition of impurities. The BOS theory shows that it is also possible

for the coherence length to be shorter than the penetration depth in pure materials with a high T , This is found to be the case in niobium (Strombexg and Swanson (

1962

)) and vanadrom (Radebaugh and Keesom (i

960

a, b))« These are the only two known elemental Type II

superconductors,

The existence of this negative surface energy in Type II

superconductors means, as one would expect, tïmt the Meissner effect

does not occur, but rather it is energetically more favourable for an *| applied magnetic field to penetrate in the form of a large number of # normal filaments. This is called the MIXED state. It is a fundamental

property of a Type II superconductor which occurs because of the negative

- I

1,5

1,3 MagnetiCvjDropextjLeB. o.f Type I superconductors

The Meissner effect in a bulk Type I ■ superconductor, that is the condition of zero magnetic flux inside a superconductor placed in a magnetic field may be considered as arising from induced surface

currents whose magnitude and direction are such that they create an internal field that just cancels out the applied field inside the specimen.

Formally we may write

Interiors % ^ ^ " 0? Surfaces

₈

_'^ 0,

Outsides B _{'-e —a —S’’}H + H , where is the field due to the surface currents.

However, since from outside the specimen it is impossible to distinguish between effects due to surface currents and those due to bulk magnetization (see for example Panofsky and Philips (

1962

) ch,

8

), we may also write

Interiors B. r= o« H. ^ 0, M 0,_{““1 ■’ ““.L ' '} Surfaces J' = 0,_{“=S ■'}

Outsides B « H + H „_{—e -"a}

_—8

where H is now the field due to the magnetization of the sample. Now B = H + M ,

And hence B^^ - 5.^^ t

M « - i H,. (1,2)

1*71

Thus this approach attributes to the superconductor an ideal diamagnetic

1

1.6

1 ,1(. B t a t e s t a t ic and d y n a iiic p ro p e rtip ia

The treatment of the previous section dealt with a long superconducting

needle in a parallel field where no complications arise due to demagnetisation

effects. Let us now consider the situation for a uniform ellipsoid of

demagnetisation coefficient D situated in an applied field parallel to

its major axis.

Standard electrodynamic trearments (Brailsford (

1966

)}, which are independent of susceptibility and therefore applicable to superconductors yield

% = % - In DM. (1.5)

Now using equation (1,2) from the previous section, we obtain

M " ? (l.Jb.a)

(l3)

Lei us now consider the special case of a sphere for which I) ^ Then,

Si =

I

Sa .

Hence we see that the induced magnetisation of the superconductor distorts che external field and the above calculations indicate that the field at the equator of the sphere will reach the criticai. value before the external field does. One is then led to the question of what happens when this OGCur's, To assume that a portion of the specimen near the equator becomes normal would lead to a contradiction. The boundary between

/ \

....

s N S N S

1

1

_{\ /} k / \ J

: I i

_{a —}

Fig, 1.1 Landau's Model of the Intermediate State,

1

1.7

arrangement of alternating normal and superconducting regions, with

B “ in the normal regions, and B = 0 in the superconducting ones.

This mixture of the two states - normal and superconducting - in the

one specimen at the same time has become known as the INTSRMBDI ATE. STATE»

It exists, in some field interval, for all geometries other than that of a long needle situated in a field parallel to its axis.

In general, the problem of the determination of the shape of the

intermediate state structure is not a simple one, and can only be, attempted if some assumptions about the shape are mad.e. The first and still the most successful theory is that due to Landau (195?) «

Landau considered an infinite plate in a perpendicular field E and assumed that it would split up into alternate superconducting and normal regions as shown in Pig. 1.1. He then found the laminar period a by

minimizing the free energy with respect to the size of the domains. There are five terms in the expression for the total free energy:

(i) the condensation energy in the superconducting domains is given by ^

2

" sT" V y ^ ' '

(il) the magnetic field energy in the normal regions is 2

given by E^

^2

“ si" W " ’ I

(iii) the energy per unit area of boundary between the superconducting t 'I and normal regions is usually denoted by o L , and in this case t' 4 we can simplify the analysis by expressing the surface energy

in terms of a characteristic length

A

such that

^ . g

The contribution of the surface energy is thus

the total free energy with respect to a /a, we find H

This just expresses the fact that the field in the normal regions is

equal to Then, minimizing the free energy with respect to a we find

,2

_ A d

a

2

2

i ( % ^o )

a a

i.e., e ? - — (

1

.

6

)

and from equation (

1

.

5

)

“ r u V h ) (1-7)

where h - ^ ^ the reduced applied field, and 0 is a numerical function

I'. ■

which has been tabulated by Lifshitz and Sharvin (I

95

I).

A typical value of 0 is 10“^ for h ^ 0.7,so for a sample 1 mm thick 1.8

i'

(iv) as shown in the figure the lines of force 'open up’ near the

*

sample surface and hence the superconducting domains become thinner* at their ends and some condensation energy is lost. This loss will be of the form

H ^ . ' if

" g f (ag/a) , .

5

where is a dimensionless function that can be computed when the exact shape of the superconducting regions is known,

(v) the spreading of the normal domains also modifies the magnetic field energy, and. this gives a term

2

^5

" ^ W o ( V ^ ) ,

where is another dimensionless function. The calculation of and is described by Landau and. Lifsbitz (

196

O).

''"''-r'y/'"- ' ■-■ - - - ' V

1.9

with surface energy parameter A-vlO"’^ mm the laminar period, should he

10

^

1

a " “

0.1

mm,

I

i

10

This, as will he seen later, is similar to that found experimentally. | The spreading of the normal laminae as they reach the surface means

that since the local field is equal to on the interface, the field in the middle of a normal laminae must drop below when it spreads out. This difficulty led Landau (19U5) to the development of a branching model in which a normal lamina was supposed to split first into two, then four laminae, etc., becoming finely divided as it approached the surface of the superconductor *

Early experiments did not show a branching type of structure

although more recent experiments have done so, (Allen and Lerski (1972 a), Solomon (

197

I), Kirohner (private communication)), This has been shown (Allen and Lerskl (1972 b)) to be in agreement with the theory of

Lifshitz and Sharvin (1951). The latter, using Landau's geometry, on

minimizing the free energy of a branching structure with respect to the | number of branches, showed that this number would be small in typical

experimental situations. This is because the reduction in magnetic gf free energy achieved through the branching is outweighed by the increase

in surface energy, .

It will be shown in a later chapter that significant branching did

not occur in the geometry used in this work, j

Various attempts to improve on Landau's model have been made. Of these, mention should be made of Andrew (19^8), who proposed a branching model where the branches were threads rather than laminae, and Kuper (1951) who developed a slightly different unbranohed model. As has been

stated, however, Landau's simple unbranched model has proved the most

successful of these and is still the most widely used, ,| ■3

I

I

a

;-1.10

The free energy of an nnlran-ched laminar structure can be lowered by

the development of corrugations in the laminae near the surface

(Faber (1958)^ Balashova and Sharvin (1957))» Like the branching

modelp this lowered the field energy at the expense of increasing the surface energy^ and Faber (1958) has presented arguments to explain why corrugations rather than branching should be observed in practice.

It should finally be stated that the differences in total free energy between the various morphologies are so small that the structure actually observed in practice often depends on how the state was achieved^ on details of the specimen shape and on specimen inhomogeneities.

The first suggestion that an intermediate state structure would move under the influence of a transport current flowing through a

superconductor was made by Gorter (1957,? 1958). He predicted that the motion would occur at right angles to the direction of the current J with a velocity

V = ^ , (

1

.

8

J

where a is the conductivity in the normal state.

The first attempts to observe this particular phenomenon produced conflicting results. 'Shar'vin (

1965

)

5

, using a point contact to the superconductor-, claimed observation of the domain motion but this experimental method was later called into question by Chandrasekhar et al (1967). A repetition of the Sharvin experiment using a superconducting microbridge magnetometer by Brandt and Parks (I967) revealed no motion of the intermediate state structm.'e.

More recently, however, motion has been observed (Solomon (19&9)? Van Gurp (I

969

)). In fact, Solomon and Harris (1971) have shown that

any intermediate state topology is unstable with respect to transverse motion in the presence of a transport current.

1.11

of noiTiial regions in a dynamic intermediate state involves a transport in entropy, and should produce a temperature difference. Conversely, temperature gradients cause a force on flux bundles and should produce

a motion just like a transport current. Equivalent effects in the

mixed state of Type II superconductors have been observed (Fiery and Serin (I

966

), Otter and Solomon (

1966

)) but until this work and the very recent publications of Gupta and Far*ell (1975) and Laeng and Rinderer (I

975

) uo experiments had been reported in the intermediate state of Type I superconductors,

1,5

Methods of observation of the intermediate state

The problem of observing the structure of the intermediate state is one of resolving the change in magnetic field (typically Oersteds) between normal and superconducting regions whose dimensions are typically of the order of 100 pm. Basically this has been accomplished

experimentally thz'ough three different methods, (a) magneto-resistance in small bismuth probes, (b) Bitter patterns using ferromagnetic or superconducting powders, and (c) Faraday rotation.

The first of these was utilised by Meshkovsky and Shslnikov (19il.7) in the first successful observation of the structure of the intermediate state. Convinced by Landau's branching theory that the flux structure would be very fine at the external surface of a superconductor, they measured the field distribution between two halves of a tin sphere. The disadvantage of this method is that the spatial resolution is limited by the size of the Bismuth probe used, and cannot reasonably be reduced below about 20 pm. Consequently, it has not been used in more recent experiments.

1,12

nickel powder onto the sample? this powder was, of course, attracted by

the magnetic field onto the normal regions when the sample went into the intermediate state, A series of rich and complex patterns was reveoJ.ed

as the external field was varied. Many subsequent experiments have been

reported using superconducting (e.g, Schawlow et al (1958, 1959))as well as ferromagnetic powders. The disadvantage of this simple powder method is that, as was shown by Olafsson (1971), the use of a powder which does not move very easily makes it difficult to obtain more than one flux distribution picture per run. On the other hand if one uses a powder which is fairly mobile (small and superconducting) then care must be

taken in the interpretation of the pattern obtained since it may represent the paths of the penetrating or escaping flux. The resolution of this powder technique has not been established, but certainly it cannot be less than several times the particle diameter

(^5

[xm.),

The resolution has recently been considerably improved through the o

method of forming an extremely fine powder (~50 A ) by means of an evaporation inside the cryostat itself, letting it drop onto the sample under the influence of the magnetic field in the normal regions. When the particles of powder fall onto the surface they become immobile and the sample can be warmed up and the pattern examined under an. optical or electron microscope. In this way, Traifble and Essmann, (I

966

a, b) and

8

arma and Moon (

1967

) have obtained pictures of the Intermediate state with the highest resolution yet obtained ( -<

0,1

p-m),

The third of these methods is based upon the fact that if a thin sheet of paramagnetic material is placed over a specimen in the

J O T D

>

II CD I— O U! U_ U_ LU

<

Q

<

C d

<

LU O LU N »— I a d < — j

o

CL < ÛL CD I

o

1— LU z CD

<

o d O Q

z

O O q: CO _J

<

O hH i-H cc:

1.15

plane of polarization from that reflected over superconducting are as ^ and

this difference may be seen with an analyser. The rotation of the plane

of polarization experienced upon passing through a thickness d of

paramagnetic material in a field H is given by Faraday's law

9 = V.H.d, (

1

.

9

)

V is called the Verdet constant of the material.

This use of the Faraday effect to observe the field distribution

in a superconductor was introduced by Alers (I

956

, 1959) and subsequently

used extensively by Desorbo et al (I

96

O, I

962

,

196

^, I

965

) and by Baird

(

196

I

4.5

1965)0

The paramagnetic material used in all these experiments

was Cerium Metaphosphate (OMP) glass from 0.2 to 0.5 mm thick. Figure

(1.2) shows a typical magneto-optic set-up. Due to the spread.lng of the magnetic field from the normal regions upon leaving the specimen, the resolution of the method is of the order of the thickness of the CMP

(Kirchner I

968

(a)) and hence in these experiments was at best

200

p,m.

An improvement of this resolution cannot simply be achieved by

further thinning of the CMP glass since, from equation (

1

,

9)3

we see that

the magnitude of the rotation of the plane of polarization depends

linearly on the thickness and hence would quickly drop below the limit of detectability. Hence, to use a thin Faraday rotator one must find a material with a very high Verdet constant. Such a material is the

ferromagnetic semiconductor europium sulphide EuS, which can be evaporated

into thin films possessing enough specific Far ad. ay rotation to render the

intermediate state visible.

The use of EuS films was pioneered by H, Kirchner

(1968

a, I

968

b,

19693

1972

) and used with varying success by other workers (Solomon and

Harris (1970), Huebener et al (1970 a, 1970 b, 1971, 1972 a, 1972 b)).

The resolution achieved by Kirchner was 0,5 pm which is quite adequate

t.-,.--;r.- T ' ' - V t f " ■ r.. » . .

-I.lii

The great advantage of this high resolution magneto-optio method

is that dynamic processes can be studied and indeed cine film or videotape

recordings of the flux motion can be obtained. None of the other methods

is capable of providing a record of dynamic processes except the magneto-resistance method and this with a much poorer resolution.

\

LN

,LHe

LN

im

II.1

CHAPTER II - APPARATUS ajid KXIERIMEMAIi DETAILS

2.1 Introduction

The resolution of intermediate state structure attainable with the magneto-optic method using europium films is limited only by the optical

system used, Eor the optical set-up in this work to be capable of

resolving the finest details of the intermediate state in Type I

superconductors it has to have a resolution of the order of

5

P-m,

Such an optical resolution can only reasonably be achieved using a

microscope, hence, in the manner of Kirchner

(1968

b), it was decided

to design a stainless steel helium dewar with optical access for a polarized light microscope.

2.2 The Cryostat

The dewar which was used (Fig. 2.1} was a modular series 100 type obtained from Thor Cryogenics Ltd. Although the main section was their standard design in stainless steel, the tail was specially designed for

this experiment. It consisted of a Stainless steel inner liquid helium

can A shaped to accommodate a superconducting magnet M described below, a copper shieId attached to the liquid nitrogen reservoir in the main section B, and an outer stainless steel can G.

The optical access was through three glass windows. The outer of

these D was made of Schott SF57 glass (for reasons to be discussed later)

and was simply glued into place using Araldite. The middle one E was made

of Chance he at : :-ab sorbing glass and was kept in thermal contact with the

nitrogen-cooled fsh,ield using GE 70)1 varnj.sh. The inner window F, again

made of Schott SF57 glass, formed the bottom of the liquid helium space

and was sealed to a stainless steel mount using an indium

0

ring carefully

II.2

to five cycles from room to helium temperatures. An important feature

of the design was that the distance from the outside of D to the sample

position G was kept below 15 mm to allow microscope objectives of fairly

high numerical aperture to be used.

The length of the tail was chosen so that the liquid helium capacity

of the whole dewar was „

5

litres, sufficient to allow for a run time

between transfers of up to I

4.8

hours when three radiation baffles were

fitted up the dewar neck.

The magnetic field used in these experiments was applied perpendicularly to the sample and was supplied by a magnet made previously in this

laboratory for another purpose. It was I

50

mm long with a bore of lj.5 mm

and consisted of 2000 turns of NbZr copper sheathed superconducting wire

wound in I

6

layers. Its calculated field/current coefficient was

I

426

Oe/Amp at its centre. •>

The current for the magnet was provided by a British Oxygen

Gryoproducts power supply which maintained the current constant to

0

.

1

%

and had safety provisions built in in the event of the magnet going normal.

The magnet current was found by measuring the voltage across a standard

one ohm resistor through which it passed with a Dynamco IM 20228 digital

voltmeter

0

The magnetic field was then determined from the calculated

field/current coefficient.

Bath temperatures between I|.,2K and 1.2K were achieved by pumping on

the helium. The temperature was obtained by measuring the vapour pressure above the bath using a mercury manometer and cathetometer or a

McLeod gauge. Two carbon resistors mounted in the helium space served

to indicate the helium level and temperature, their resistance being

measured with an Oxford Instruments AG resistance bridge which dissipates

less than 10” in the resistor.

Indium

Seal

L H e

Current

Lea(^;

Spring

Sample

W i n d o w with EuS:EuF^ film

Fig, 2,2. 8ample mount for the observation of current-induced flow.

Copper

L H e

Current

Leads

Perspex

Ctr—

C Z Jb

'2ZZ/!ZxAr-

Heater

^ S a m p l e

‘W i n d o w with EuSiEuF^ film

- II.3

purap the vacuum insulation space of the dewax* to a pressui.*e of less than

10 torr before helium transfer when the dewar was sealed off. The

avoidance of diffusion pump oil coating the dewar windows was ensured by the use of a stainless steel liquid nitrogen-cooled trap on the diffusion

pump.

2.5

Oon struct ion of the sample mount

(i) For the observation of current-induced flow

As will be shown later, to obtain meaningful results for current-induced

flow it was necessary to ensure that the superconducting sample was in good

thermal contact with its surroundings. The samples were consequently

pressed against the EuSsEuF^-coated inner window from inside the liquid helium space and hence were immersed in liquid helium.

Fig. 2.2 shows the details of the sample mount. All samples were thin slabs of approximate dimensions 1 0 m m x 5 m m x 2 m m thick. Good contact between the sample and the magneto-optic mirror was ensured by the use of

a non-magnetic stainless steel spring (made from 18 gauge wire) which

pressed them together. The leads for passing a current through the sample

were soldered to its ends with indium and were made from copper coated

NbTi filamentary superconducting wire. After a length of about 10 cm these wires were soldered to 20 swg copper wires which led up to the cryostat top.

Currents up to 10 amp could be passed through these leads using a

Farnell L

3

OF power supply which held the current constant to better than I/o.

(ii) For the observation of thermally-induced flow

It was necessary in this case to mount the sample so that a known temperature gradient could*-be established along it and a current passed

through it. Fig. 2.3 shows how this was accomplished.

All of the samples were thin slabs of dimensions 15 mm x 5 mm x 2 ram thick. One end of the sample was screwed to a copper post mounted at the

Pb

Heater

Pigo

2

aij. Arrangement of the thermometers and heater on the

II.k

perspex post, which had a heater resistor inserted in it. Good thermal

contact between the copper post and the sample was ensured by soldering

them together with Woods metal. Good thermal contact with the heater was

accomplished using GE 7031 varnish. The heater used was a 1KS2 carbon film

resistor, this type being chosen because the resistance changes very little in the liquid helium temperature .range.

The disc of SP 57 glass bearing the europium film was located in a perspex mount which was then firmly screwed down against the sample, A copper heatshield with a small hole to allow observation was attached to the copper post and surrounded the sample mount.

As in the last case the leads supplying a current to the ends of the sample were of EbTi superconducting wire. These were soldered with indium, to the sample and were passed through a glass/metal seal in the copper mount up into the liquid helium bath.

Temperatures at two points on the sample (Pig. 2.4) were measured

using 100 Q Allen-Bradley resistors of dimensions I

4

xmn long x 1 ram diameter;

these being the smallest available. The resistors were varnished to the

underside of the sample using GE 7031 varnish. Their resistance was measured with the Oxford Instruments AC bridge. The leads from these two

resistors were of thin (38 swg) silk-covered constant an wire. These were

thermally anchored to the copper post with GE

703

I varnish after a long

coil to ensure good thermal isolation from the bath. The leads to the

.heater were of 36 swg enamelled copper wire and were similarly treated. All these leads were taken to the outside at the base of the cryostat, being thermally anchored to the nitrogen shield with GE

703

I varnish on the way.

The power for the heater came from a Parnell L3OA power supply, 500 rnW being the maximum power required.

î

II.5

2,1|. Requirements of the magneto-ont.lc experiment

The main disadvantage of EuSsEuP,. films is their large absorption #

S

-1

%

coefficient of 2 x lO^^cm™' (Suits and Argyle (

1965

)); this limits the i thickness that can be used and hence the rotation attainable. In the

o

present work all the films used were about 2000 A thick and transmitted

about

25

% of the light incident upon them.

Suppose in a particular situation a rotation 0^ of the plane of polarization of the incident light is obtained. On analysis the

I

2

y

intensity of transmitted light is reduced by a factor cos 0^, and since ;|

'i 6^ is typically 30', the intensity loss through absorption in the film and

analysis of the light is 99«8%» Consequently, if sufficient light is to

be left for examination, a light source of high intensity must be used and

the illumination, of the sample must be as efficient as possible.

Obviously the resolution attainable by this method is limited by the

film thickness, the contact to the sample, and the optical system. The

film thickness is 0,2 pm and the sample surfaces can be pressed or polished flat to

0,5

fxm so that in practice the largest limitation on the resolution is that of the optical system,

Martin (I

966

) has given the resolution limit of a microscope objective as

\ - l y r x j »

where X is the wavelength of the light in use,

Aq is the numerical aperture of the objective, and

A is the numerical aperture of the condenser.

Hence the objective must be chosen to have the highest numerical aperture

given that the limitation of the working distance is a minimum of 15 mm.

Care must also be taken with the condenser system.

The contrast between normal and superconducting regions depends on thu

II.6

for a contrast to appear' is that the intensity of rotated light must exceed

the overall intensity of light passed at the extinction 1^ , i.e..

_E , of various polarizers and analysers. They found values of ~ 10~ for

lo

the best available diohroic polaroid sheet, Kasemann MIK, Substituting in the above equation we see that the smallest 0^ discernible, ignoring strain ellip^city, is about four minutes of angle. However, the presence of

5

strain can easily increase the extinction ratio to as high as 10 and this dramatically raises the smallest 0^, discernible to almost 2°, Hence,

clearly the best quality polaroid must be used and extreme care must be

taken to minimise strain in the system.

King and Talim also showed that the avoidance of dust and extreme

cleanliness are important if a high extinction ratio is to be maintained.

Now the window into the helium space and the outer window both form vacuum seals and hence are unavoidably under strain. To minimise the effect this strain would have on the state of pclai'ization of the light passing through them, a glass with a low photoelastic constant was chosen for their

construction. The photoelastic constant of a glass relates the

birefringence produced in the glass to the applied stress (Hendry (I

966

)).

This glass was obtained from JENAer Glaswerk Schott and Gen. under the

Code No. SP57o Its maximum birefringence is 2 nm/cm and its refractive

index is 1.85. Both windows were made from discs 1.5 mm thick, the inner

window being

15

mm in diameter and the outer 25 rrm in diameter.

The magnitude of Ig depends on two factorss (a) the practical limit

to performance of the polarizer and analyser, and {'bj any ellipticity in the

state of polarization due to strain in the cryostat windows or microscope #

objective. King and Talim (1970) have measured the extinction ratio .--i

11,7

2 ^ 5 Preparation of the EuSgEuF^ films

Kirchner (I968 a) found in the course of his development of the use of

europium films that a pure EuS film, since it is ferromagnetic below 16k

(Ens et al (I962)), perturbs the intermediate state structure of the

superconductor. He showed, however, that a mixed film of EuS and the paramagnetd.c material EuEg did not have a ferromagnetic transition in the

temperature range of interest although it still exhibited a high Faraday

rotation, Laeng and Rinderer (1972) have shown that the proportions of

Bus and EuFg in the mixture is vitally important'«if alterations to the

intermediate state structure are to be avoided. They found that EuSsEuF^

in the proportion 2s3 was most suitable and this was the proportion used in

the present work.

The evaporation technique used was similar to that of Kirchner (private communication). The films were evaporated onto the SF57 glass inner window against which the superconducting samples would be pressed, EuS obtained from Dr, Kirchner and EuFg obtained from K 6 K Labs,, New York, were mixed together in the proportions indicated above. They were then placed on a

tantalum boat 0,01 mm thick in a standard high vacuum coating unit, A shutter

between the boat and the substrate was used during degassing at a boat

temperature of about 750^0, The evaporation was then performed at a boat

temperature of about 2300°0, The process was essentially a ’flash* one;

the evaporation was over in a few seconds, with the pressure being always held below 2 x 10”^ torr. Four or five such evaporations were needed to

achieve a film of the required thickness, the vacuum being broken to replenish the boat each time.

It was found vitally important to use stainless steel fittings in the coating unit since the high boat temperature produced contamination due to

zinc sublimation when brass fittings were used. An EuSsEuF^ film contaminated

with zinc had an increased optical density and produced no measurable

Objective

Eyepiece

Illuminator

Analyser

Ê t

%

j

II.8

absence of rotation would not be expected if the only effect of the sine were to increase the absorption of the film. Hence, the presence of the

zinc-m u st, in sozinc-me zinc-manner, have d e s tro y e d th e zinc-m agnetic p r o p e r tie s o f th e f ilzinc-m .

T h is phenomenon was n o t in v e s tig a te d f u r t h e r .

The f ilm th ic k n e s s was c o n tr o lle d by m easuring th e f ilm a b s o rp tio n w ith

a Pye spectrophotometer and using the data of Suits and Argyle (I

965

),

o

An aluminium film of 1000 A thickness was then evaporated on top of the Eu8:EuPg film to complete the magneto-optic mirror,

2,6 Optical equipment

The re q u ire m e n ts o f th e m a g n e to -o p tic expe rim en t were n o t met by a #

g

single commercially available microscope; in consequence a microscope had i

to be assembled from various component parts as shown in Fig,

2

,

5

,

The restriction of the cryostat design (i.e. the insert tube) meant that the illumination of the sample had to be accomplished through the

microscope objective; an. incident illuminator was obtained from Vickers Ltd. for this purpose. This was specially designed to minimize the introduction of ellipticity into the polarized light by using two acute angle reflections to deviate the light.

The anal.yser w^as also obtained from Vickers, It contained a sheet of KKsemann MIK polaroid mounted between two strain-free pieces of glass.

As s ta te d in a p re v io u s s e c tio n t h i s was th e b e s t a v a ila b le d io h ro ic

P o la ro id sheet a c c o rd in g to th e d a ta o f K in g an.d T a lim (1970). The

o r ie n t a t io n o f th e a n a ly s e r c o u ld be re a d to 0 .1 ^ by means o f a v e r n ie r s c a le .

A fte r r e f le c t io n fro m a m ir r o r mounted in a machined b ra s s jo in t in g

p ie c e th e l i g h t e n te re d a d ouble e yepiece h o ld e r a ls o o b ta in e d fro m V ic k e rs ,

One eyepiece was used f o r v is u a l o b s e rv a tio n , th e o th e r f o r p h o to g ra p h ic w o rk .

The eyepiece used f o r v is u a l o b s e rv a tio n was o b ta in e d fro m E , Leitz GmbH and had a magnification of 6.3x. The eyepiece used for photogi'aphic work was o b ta in e d fro m R e ic h e rt We in GmbH and had a m a g n ific a tio n o f

Table 2,1 Microscope Objectives,

Nominal Numerical Resolution Working

Manufacturer Magnification Aperture Limit Distance

(pm)

( i) Ealing Beck

2

0.08 3.1 U5

( ii) Vickers 3

0.1

2.5 35

I

II.9 %

4y

The four objectives used in the course of this work are listed in -r

Table 2,1 together with their specifications. The resolution limits are o

calculated for light of wavelength 5^81 A, All the objectives were types %

designed for use with polarised light, their mountings being strain-free.

Most of the observations were made with the x3 objective (No. ii), and hence

the magnification usually employed was about 30. A graticule obtained from ii

belts, which divided the field of view into sixteen squares, served to provide a quantitative measurement of the observed structure sizes, the

calibration standard used being a stage micrometer of one hundred 10 pm

divisions obtained from J, Swift Ltd,

The whole microscope was mounted on an optical bench stand made by Baling Beck Ltd,, which incorporated provision for vertical motion for

focussing purposes, and for horizontal motion along and perpendicular to the

optical bench for alignment on the correct part of the sample. The

construction of this stand was made as rigid as possible to reduce shaking of the microscope whilst in use.

As previously stated the light source used in these experiments had

to be of high intensity and the illumination of the sample as efficient as

possible. Since the highest rotation of the plane of polarization by

europium films occurs at short wavelengths (Suits and Argyle (

1965

)) a blue or green light source Was required,

o

An attempt was made to use a HeCd laser wbich emits at 14.800 A, but this proved unsuccessful due to interference effects obscuring the required

picture,

A high pressure mercury discharge lamp (Osram HBO 200) was then

successfully used. This was obtained from Leitz mounted in a housing with

provision for focussing and collimating the beam to give the maximum possible

intensity input to the microscope system. The main wavelength emitted is

0 o £

CD o o

1 CJ - I

w

Ui

a

UJ

Q.

V

o

UJ

o

a.

UJ

UJU.

>

■5ZZ.

I

Q.

=J

I -M_<D

m

in

O

1

I

"O_c a

a o

-j-"

CL

O

CD

(N

vy^'-v , <;•

II oK

4

5

ultra-violet which are also emitted. The estimated luminous flux entering

the polarizer was ~

3000 lumens,

To preserve this high intensity input to the microscope as much as

possible a nicol prism was used to polarize the beam. This has a low loss |

(10%) compared to high quality diohroic polaroid which absorbs 70)(, of the -g incident light. This nicol prism was made by Bellingham s Stanley Ltd,

and was incorporated in a mounting which enabled its orientation to be

adjusted and measured to 0,1°, This mounting also served to improve the ■ y

■■ f

collimation of the beam before it entered the microscope,

As previously mentioned, the small rotation and high absorption of the europium films lead to very little of the light incident from the lamp emerging from the eyepiece for observation. For photographic purposes the emergent light is in fact insufficient to produce a high contrast fine grain

record of the flux distribution. Consequently, an image intensifier .jJ

(Mullard Type XXIO5O) was used to amplify the light level to improve the îï

o , ^

photographic results. This had a gain of ^ 95 at 5^81 A and was mounted in

a specially designed casing. Fig, 2,6 shows its construction. The outer ;

brass casing connected to the cathode served as a screen to minimize the i

background illumination. The resolution of the intensifier device at 60

line pairs/mm was such that it introduced no image degradation, A high

voltage

(15

kv) was required for the image intensifier and this was supplied

by a Brandenburg 7?6A encapsulated power supply driven by a Hewlett Packard

6 2 Q Ï X variable DC power supply.

All still photographs were taken with a Nikon F 35 mm single lens reflex camera. When used with the image intensifier, bellows and a Nikon

50

mm f/2 lens were used to give a reproduction ratio of about /2, When

the image intensifier was not in use the microscope eyepiece was used to project the image directly into the camera with lens removed.

Some

16

mm cine film was taken using a Bo lex HI

6

camera. This was

h = 0.4

100um

I - -4

h = 0.6

11.11

The complete optical and cryostat set-up is shown in the diagram of

Fig, 2.7(a) and the photograph of Fig, 2,7(b), As can be seen in the

photograph the dewar was mounted on a frame welded together from

1

" box

steel section with two steel optical benches being bolted to the frame

beneath the dewar to carry the optical equipment. The whole structure

was bolted to the floor and wall of the Laboratory to increase its rigidity.

Another small frame by the side of this frame carried the electronic equipment whilst the vacuum equipment was mounted on a 'Unistrut* frame behind the main frame,

2 ,7 Performance of the apparatus

The optical apparatus performed in general very well and the resolution achieved was certainly of the same order as the theoretical prediction.

The photographs of Fig, 2,8 illustrate the quality of intermediate state pictures obtained. The magneto-optic contrast was such that observations could be made with critical field values as low as 9^ oersted. This is quite sufficient to allow the study of the superconductors Pb (H^ - 803 Oe),

Sn (H - 309 Oe), and In (H^ - 293 Oe), Greater field sensitivity could

have been achieved by increasing the film thickness slightly, but this was not found to be necessary for this work.

The long run-time possible with the stainless steel dewar was advantageous when the experiment was functioning correctly but the

consequently long time necessary to preoool before helium transfer led to long turn round times for simple adjustments to the experimental structure. Recent advances have^ however^ given continuous flow systems which have

turn round times of „

1

hour and these would perhaps be more convenient

A M M E

T E R

S A M P L E i

N A N O V O L T M E T E R

,/ I/V. ■ ' : O ' -i ' ' - ' / X

11.12

2.8 Meagurement of the aample condiictivit:/

The normal state conductivity of the materials used in the magneto-optic

experiment were measured using a conventional four terminal technique

(Fig. 2.9).

The voltage across the sample was measured using a Keithley 1[|.9

nanovoltmeter, the current through the sample being provided by a 2V

accumulator and measured with an Avo multimeter. The experiment was

performed in a large glass helium dewar previously built in this laboratory.

A small superconducting magnet of computed field/current coefficient

320

Oe/amp was used to supply a magnetic field large enough to quench the

superconductivity when measurements were being taken, the field being applied transversely to the wire.

As in the other experiments the current for the superconducting magnet was supplied by the British Oxygen. Cryoproducts power supply, its magnitude being measured in the same manner as before.

Temperatures between ^.2K and 1.2K could be obtained by reducing the pressure above the helium bath. The pressure above the helium bath was measured with a simple manometer for pressures not much below atmospheric or with a McLeod gauge for low pressures.

Due to the high purity, 6-9’s, of all the metals used it was found

impossible to produce a measurable voltage across the same samples that were

used for the magneto-optic experiments. Consequently, wires of ~ 1 mm diameter were used in the conductivity measurements, the leads being

attached to them using indium as a solder. In the case of Pb and In these

wires were extruded from the same batch of metal as was used to make the

11.13

In all these measurements it was found to be very important to apply the correct magnetic field to just quench the superconductivity and not a bigger one since all these metals exhibit appreciable magneto-resislance at the temperatures used (Olsen (I962)).

The calculation of the conductivity from the measured resistance

requires a knowledge of the ratio of the wires length to its average area.

This was calculated by measuring their resistance at room temperature

(with a small current to avoid Joule heating) and using values obtained

in the literature for the room temperature resistivity. The ratio obtained in this manner agreed with that directly measured using a micrometer and caliper gauge to within about 10#. The value obtained from electrical measur'ements was, however, used since it was considered

that it represented a more reliable average value that that based on

H^(Oe)

Indium 3.iiO 293

Lanthanum 6,0 l600

Lead 7.18 803

Mercury u a.15 u n

P 5.95 3U0

Tantalum U.U8 830

Thallium 2.39 171

Tin 3.72

509

III.l

CHAPTER III - SAMPLES

I

301 Introduction

There exist seven Type I superconducting metals whose transition

temperatures are in the range 1,2K to U«2K as shown in Table 3«1.

Lanthanum and mercury are difficult to handle, the first because of rapid

oxidation in air and the second because it is, of course, liquid at room ||

temperature. Tantalum has a high melting point (2832°C) and is very hard, making the production of samples difficult. This leaves indium,

lead, thallium and tin; all are soft with low melting points and hence are

easily pressed or cast to any desired shape.

In the present work all were used except thallium which was excluded

because it could only have been used in the restricted temperature range

1.2

K - ^

2.

2

E.

The importance of the recognition of the existence of magneto-resistance in these materials during the conductivity measurements has already been mentioned in Chapter II. The competing nature of this magneto-resistance

and the intrinsic temperature dependence of the resistivity means that the

effective conductivity important in the present work (i.e. that in a field

H^) has a different temperature dependence from the zero field conductivity.

Indeed, after the resistivity has reached the residual value the magneto- re si stance effect can produce a slightly increasing resistivity as the temperature f alls.

The conductivity values were corrected to give those appropriate to

the slab samples instead of the thin wires (Newhouse (

196J

4)). This

necessitated the assumption of values for the bulk electron mean free path at ij..2Ko For Pb this was taken to be ^ x 10 '^cra (Cody and Miller (1968a)),

for Sn 8 X 10"^om (Cody and Miller (1968b)), and for In 1.6 x 10 ^om

BXPERIMEWT DIMENSIONS (mm) <j ME AS . (mhos,cm

T = b.2K

Pb 1 Current-induced

motion

Pb 2 Thermally-induced

motion

Pb 3 Thermally-induced

motion

Pb i|. Thermally-induced

motion

Pb 5 Current-induced

motion

6 X 5 ^ 1.1| thick

13

X 3.9 % 1,1 thick

15 X 6.5 X 1,8 thick

15

X 5.6 X 1,5 thick

6 X 5 X 1.4 thick

(Ü.1 - 0.3) X 10‘

III.2 S ; the samples used In these other studies yielded very similar values for

the hulk resistivity at The calculated corrections amounted to i;

\ % for Ph, 9% for Sn and 5% for In. :!

I

5 o2 Lead |

The magneto-optic contrast is, as was shown in Chapter II, best for high fields and hence the observation of the intermediate state was most easily performed using lead which has a high critical field in the available temperature range. This was, consequently, the material used most

throughout the present work.

The metal which was used to make all of the samples was obtained from Kbch-Light Laboratories in the form of small shot of 99.9999# purity. The

slab samples were produced by pouring the molten lead from a porcelain

crucible into a stainless steel mould. The inside of the mould was coated

with 'Acheson' colloidal graphite to inhibit sticking of the lead and to

avoid it making contact with the stainless steel. Careful preheating of

the mould to a temperature above the melting point of lead (

326

°C) and slow

cooling of the mould from its bottom after insertion of the lead, ensured

that the resultant slab contained fairly large crystallites.

After removal from the mould the slab of lead was chemically polished in a mixture of four parts glacial acetic acid to one part of hydrogen peroxide (100 vol.). Its faces were then pressed flat by squeezing them

against quartz flats in a hydraulic press. The quartz flats were obtained

from Jencons Limited and were guaranteed flat to X/8 across their diameter

(15

mm)0

Table 3.2 gives the characteristics of the five lead samples used. The resistance ratio of the metal used (^300) was 9300 - 100, Samples

pbl). and Pb5 were annealed at

260°0 under a vacuum of <10 torr for

EXPERIMENT

Sn 1 Current-induced motion

In 1 Current-induced motion

DIMENSIONS (mm) g MEAS.

(mhos, cm )

T = k o 2 K

6 X 5 X 1.5 thick (6,6 - 0.5) % 10

6 X 5 1.5 thick (2.5 ~ 0.2) x 10^

III.5

Tb.e intrinsic temperature dependence appeared to just dominate the

behaviour of the effective conductivity below i^.SK since a slight increase

of 5% occurred between this temperature and I.5E,

3.5 Tin

The tin was obtained from Metals Research Ltd. in the form .of 0.5 mm

wire of 99«999% purity. The slab samples were produced by melting this rsg

wire in the stainless steel mould as with the lead,

Chemical polishing was done with dilute hydrochloric acid and the faces of the sample were again pressed flat against quarts flats in a

hydraulic press. After pressing, the samples were sealed in Pyrex tubes

pumped to a pressure of less than 10 ^ torr and annealed at a temperature *3

of l60°C for ij.8 hours to remove strains.

Table 3»3 gives the characteristics of the one tin sample used.

The resistance ratio (R^^^/R^ of the metal was 7200 - I50.

In agreement with the conclusions of Laeng et al (l97l), the effective

conductivity of the tin was found to decrease slightly as the temperature

fell below its transition temper at ur'*e due to the effect of transverse

magneto-re si stance. The value at the lowest temperature (1,3%) was

12.

5

% lower than that just above T^.

3 Indium

The indium was obtained from Johnson Mat the y Ltd, in the form of a

polycrystalline rod of 99*9995# purity. The slab samples required were

produced by squeezing sections of this rod (cut with a sharp stainless steel blade) in the hydraulic press.

The polishing and surface preparation was identical to that described above for Sn. No annealing was considered necessary since indium

re-crystaliises readily at room temperature.